To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

-7y - 1 = 2 - y
-7y = 2 - y + 1
-7y + y = 2 + 1
-6y = 3
y = \( \frac{3}{-6} \)
y = -\(\frac{1}{2}\)

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{64} \) = 8

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 8² + 8²
c² = 128
c = \( \sqrt{128} \) = \( \sqrt{64 x 2} \) = \( \sqrt{64} \) \( \sqrt{2} \)
c = 8\( \sqrt{2} \)

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -64 as well and sum (Inside, Outside) to equal 0. For this problem, those two numbers are -8 and 8. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 64
y² + (-8 + 8)y + (-8 x 8)
(y - 8)(y + 8)

A trapezoid is a quadrilateral with one set of parallel sides.

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

b² - 20b + 58 = -5b + 2
b² - 20b + 58 - 2 = -5b
b² - 20b + 5b + 56 = 0
b² - 15b + 56 = 0

Next, factor the quadratic equation:

b² - 15b + 56 = 0
(b - 7)(b - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 7) or (b - 8) must equal zero:

If (b - 7) = 0, b must equal 7
If (b - 8) = 0, b must equal 8

So the solution is that b = 7 or 8